Capital - in particular of the physical sort - plays several roles in economic life: it constitutes wealth and it it provides services in production processes. Capital is invested, disinvested and it depreciates and becomes obsolescent and there is a question how to measure all these dimensions of capital in industry and national accounts. This revised Capital Manual is a comprehensive guide to the approaches toward capital measurement. It gives statisticians, researchers and analysts practical advice while providing theoretical background and an overview of the relevant literature. The manual comes in three parts - a first part with a non-technical description with the main concepts and steps involved in measuring capital; a second part directed at implementation and a third part outlining theory and a more complete mathematical formulation of the measurement process.

Welcome to the revised OECD Manual Measuring Capital. This Manual should be of benefit to both producers and users of capital statistics. The publication of the original Measuring Capital Manual in 2001 was a significant development in the statistical measurement of a vitally important component of economic activity. Capital plays a fundamental role in the process of production and it is a significant component of wealth and source of income. It is vital that both stock and flow aspects of capital are well measured in order to support the development and monitoring of economic policy, as well as economic analysis more generally. This revised edition of Measuring Capital builds on the original version, by taking account of new developments in capital measurement and ensuring consistency with the revised System of National Accounts – the 2008 SNA.

This Manual benefitted significantly from contributions of members of the Canberra II Group on the measurement of non-financial assets and from thoughtful comments provided by national statistical offices, in particular Statistics Canada, the U.S Bureau of Economic Analysis, Statistics Netherlands, Eurostat and the German Federal Office of Statistics. Special thanks go to Erwin Diewert (University of British Columbia) and Koji Nomura (Cabinet Office of Japan and Keio University) for many insightful comments, corrections and suggestions of draft versions of the document. Thanks are also due to Dale Jorgenson (Harvard University) and Chuck Hulten (University of Maryland) for their support during the gestation period of the Manual. All errors remain with Paul Schreyer (OECD), the principle author of the document.

It may be helpful to briefly recall the role that capital plays in a stylised system of national accounts. This can easily be done with a circular flow diagram, as shown in the figure below. Flows of quantities of goods and services are matched by monetary flows. In the simplest case with only consumers and producers, the basic exchange is between labour (hours worked) and consumer products. These are exchanged in the markets for labour and for consumer products and give rise to revenues and costs for producers, and expenditure and labour income for consumers. The flow of labour into the producer’s sector and the flow of consumption goods out of it signal a production process whose analysis is central to many economic questions.

One of the main objectives of the present Manual is to present an integrated and consistent approach towards capital measurement that encompasses different measures of capital stocks (gross, net and productive stock) alongside with the relevant measures of economic flows (investment, depreciation and capital services). Capital stock featured in two places in the 1993 SNA, as part of compilation of balance sheets and as a tool to derive estimates of depreciation or consumption of fixed capital (CFC). How is gross capital stock estimated? Basically by cumulating gross fixed capital formation (GFCF) year by year and deducting retirements. Because it makes no sense to aggregate expenditures undertaken in different years without adjusting for the difference in prices between those years, all capital stock figures are in “constant prices”. These prices may be the prices of the current year, in which case past expenditures are adjusted to the current price level or may be expressed at the prices of a given year, usually the one which is the base year for constant price national accounts.

The central economic relationship that links the income and production perspectives to each other is the net present value condition: in a functioning market, the stock value of an asset is equal to the discounted stream of future benefits that the asset is expected to yield, an insight that goes at least back to Walras (1874) and Böhm-Bawerk (1891). Benefits are understood here as the income or the value of capital services generated by the asset.

In what follows, we shall consider a single asset, although this is clearly unrealistic: no firm, and much less a statistical agency will measure capital by looking at individual pieces of machinery or equipment. The typical case is to consider classes of assets, although an attempt is normally made to keep these classes of assets as homogenous as possible. For the moment, however, consider a single asset that is new, i.e. of age zero.

To this point, only a single asset has been considered. This is unrealistic because in practice, data exists only on classes and cohorts of assets. A class of assets brings together similar assets, for example in line with a product classification. A cohort of assets exists when many units of the same asset are invested during a particular accounting period. Even when identical assets are purchased at the same point in time, it is unlikely that they are all retired at the same moment.

Depreciation is the loss in value of an asset or a class of assets, as they age. Depreciation is a flow concept and as such shares key features such as principles of valuation with other flows in the national accounts. Economically, depreciation is best described as a deduction from income to account for the loss in capital value owing to the use of capital goods in production.1 The meaning of the value loss in production explains also why “Consumption of fixed capital” (CFC) has been used as a synonym for “Depreciation” in the 1993 SNA. Similarly, in the United States national accounts, the term “Capital consumption” has been employed.

The stock of assets surviving from past periods, and corrected for depreciation is the net or wealth capital stock. The net stock is valued as if the capital good (used or new) were acquired on the date to which a balance sheet relates. The net stock is designed to reflect the wealth of the owner of the asset at a particular point in time. Hence, the notion of “wealth” stock which seems more telling than ‘net’ stock because there are other types of “net” capital measures, for example the productive stock is ‘net’ of efficiency losses of capital goods due to ageing. The net stock is the measure that enters balance sheets of institutional sectors.

The stock of a particular type of assets surviving from past periods, and corrected for its loss in productive efficiency is the productive capital stock1. Thus, productive stocks are directly related to the quantity and production aspect of capital. Productive stocks constitute an intermediate step towards the measurement of capital services. The assumption is made that the flow of capital services – the actual capital input into production – is proportional to the productive stock of an asset class. If the factor of proportionality is constant, the rate of change of capital services will equal the rate of change of the productive stock2. The same rate of change constitutes the volume component when it comes to splitting the change in the total value of capital services at current prices into a price and a volume component. A different way of seeing the productive stock of a particular type of asset is as the embodied volume of current and future capital services. The concept of a productive stock is only meaningful at the disaggregate level of a particular type of asset. Once each asset’s productive stock is combined with the corresponding capital service price (per unit of the productive stock), the resulting value represents the flow of capital services. This is the relevant variable for aggregation across different types of assets.

In a production process, labour, capital and intermediate inputs are combined to produce output. Conceptually, there are many facets of capital input that bear a direct analogy to labour input. Capital goods are seen as carriers of capital services that constitute the actual input in the production process. For purposes of productivity and production analysis, then, capital services constitute the appropriate measure of capital input. At present, however, the national accounts provide no measure of the value, price or volume of capital services.

Consumption of fixed capital or depreciation is sometimes thought of as reflecting the full costs of using fixed assets. That this is a misconception can easily be shown by taking the case where fixed assets are not owned by a firm but rented from another unit who owns the capital good. The owner’s price charged for the rental will comprise not only depreciation (consumption of fixed capital), but other elements as well, for example an item reflecting financing costs of capital, lest the asset owner would make a permanent loss from renting out the asset.

Most but not all of the stock and flow measures considered in this Manual relate to “produced”, non-financial objects (fixed assets and inventories) that are included in gross capital formation as defined in the national accounts. Produced non-financial assets come into being via the production process or as imports.

Table 9.1 gives the full listing of non-financial assets recognised in that system. For a treatment of other natural resources such as subsoil assets, the reader is referred to the Handbook on Integrated Environmental and Economic Accounting (United Nations et al. 2003) and to Section 18.3. Note that two items related to non-produced assets are part of the produced assets. These are major improvements to land and costs of ownership transfer on non-produced assets.

The perpetual inventory method (PIM) is the most widely used approach towards measuring stocks and flows of fixed assets. It rests on the simple idea that stocks constitute cumulated flows of investment, corrected for retirement and efficiency loss. The basic sequence of implementation is shown in the figure below.

Two entry points exist into the computation process: by defining the age-efficiency profile for each type of asset (starting point A) or by defining the age-price/depreciation profile for each type of asset (starting point B). The next step is to define a retirement profile with its parameters, among them the average and the maximum service life. The retirement profile is combined with the age-efficiency profile (path A) or with the age-price profile (path B) to yield an age-efficiency/retirement profile for a cohort or an age-price/retirement profile for a cohort. In the case of geometric depreciation, the two profiles coincide and the implementation process starts only here.

The age-efficiency profile of a single asset describes the time pattern of productive efficiency of the asset as it ages. The specific form of the age-efficiency profile is an empirical issue although solid empirical evidence is scarce and often replaced by plausible assumptions. The age-efficiency function of a single asset reflects losses in efficiency due to wear and tear as well as certain effects on service lives. For example, if obsolescence affects an asset’s economic service life – e.g., because secular rises in energy prices or real wage increases make it unprofitable to use an asset after a certain number of years – this may affect the maximum service life, a parameter of the age-efficiency function. Obsolescence could then imply retirement of an asset, which amounts to an unchanged age-efficiency function up to the point of retirement and a drop to zero at this point.

In this document, consumption of fixed capital or depreciation has been defined as the loss in value of an asset due to physical deterioration (wear and tear), and due to normal obsolescence. Depreciation is a value concept, to be distinguished from quantity concepts such as the age-efficiency function that capture losses in an assetfs productive efficiency. There are several ways of determining depreciation parameters. They include:

Start from empirical information about assets' service lives, and make an additional assumption about the functional form of the depreciation pattern. The various approaches towards assessing service lives empirically are described in Section 13.1; Use information on depreciation implicit in used asset prices and exploit it econometrically; Derive age-price and depreciation patterns from age-efficiency profiles; Use a production function approach and estimate depreciation rates econometrically.

4. The first two methods are by far the most common ones and will be described in some detail below. The production function approach will be described very succinctly.

The accuracy of capital stock estimates derived from a PIM is crucially dependent on service lives – i.e. on the length of time that assets are retained in the capital stock, whether in the stock of the original purchaser or in the stocks of producers who purchase them as second hand assets. Note that the asset life is understood here as an economic notion,1 and not as a physical or engineering notion of capital goods. This is important because it implies that asset lives can change over time simply due to economic considerations even if the asset remains physically unchanged. In fact, economic service lives are one avenue by which obsolescence manifests itself – the decision to retire is taken because a new and possibly more productive and/or cheaper asset appears, rendering the old model obsolete.

More precisely, the average or mean service life has to be distinguished from the maximum service life of a cohort of assets because the service lives of the same assets within a cohort are normally described by a retirement or mortality function, more of which below. The first section below looks at the sources that are available to estimate service lives, the next section considers evidence that service lives may be changing over time, and a final section looks at how errors in service life assumptions may affect reliability of capital stock estimates. Annex 1 shows the service lives used by several countries.

Whatever the specific way of implementing measures of capital services and capital stocks, one of the key ingredients is investment data. Investment data should be broken down by type of asset and by economic activity. The level of disaggregation should be as detailed as the data allows and distinguish in particular those capital goods whose purchase prices follow different trends. Likewise, the industry break-down is important if it is believed that asset compositions vary greatly between industries and/or different industries face different depreciation rates, required rates of return and purchase prices of capital goods.

At this point, the following elements should be available: an age-price and an ageefficiency profile for cohorts of particular types of assets; a depreciation profile which constitutes a direct transformation of the age-price profile and time series of gross fixed capital formation at constant prices as well as the corresponding deflators. With these elements in hand, the computation of the net stock, the value of depreciation, the productive and the gross capital stock is relatively straight forward. However, there is a practical issue that we have so far neglected – the periodicity of calculations. In most of the discussion above, allusion was made to “a period” or “a year” signalling that annual periodicity has been the implicit guide for presentation. And annual frequency is indeed the typical periodicity for capital stock measures in national statistical offices. But of course, quarterly national accounts exist and, if anything have become increasingly important in recent years. Even if balance sheets of the economy are compiled annually, flow measures such as depreciation should have their place in quarterly accounts and their calculation depends on measures of the capital stock. Moreover, a central aspect of capital services measurement is the possibility for a complete decomposition of the income side of the national accounts into price and volume measures and implementing such a pricevolume split at quarterly rhythm should at least be a medium-term objective. In principle, it is possible and should suffice to present a quarterly model for computations, along with the relevant formulae for annual data derived from quarterly variables. For many countries, this may be an unrealistic way forward, however, given data availability. For this Manual, we shall not venture into a presentation of quarterly measures and only short reference will be made to sub-annual calculations below. Otherwise, the presumption is that a period corresponds to one year.

Part I of this Manual (Section 8.3) discussed the conceptual foundations for the computation of rates of return. Two main approaches (ex-post, endogenous rates and exante, exogenous rates) can be found in the literature, each with its advantages and drawbacks. The Section at hand will provide more details for all three avenues towards measuring the rate of return.

To this point, most of the discussion has been conducted with reference to a single (type of) asset. Many concepts are indeed best conveyed in this manner but aggregation plays an important role in how the concepts of productive stock, capital services, net stock and capital composition translate into measurement.

The single most important point in this context is that it is the process of aggregation that essentially shapes the difference between capital services and the net or wealth capital stock. At the level of individual assets, the productive stock may differ from the net capital stock but not necessarily so. The most important case where the two measures coincide is in the presence of constant, geometric rates of depreciation which imply the same rates of efficiency decline and hence identity between productive and net stock at the asset level. However, for all types of age-efficiency and age-price profiles, when the productive stock is multiplied through by an expression for unit user costs, a difference arises between the value of the net stock and the value of capital services. This difference carries through in the aggregation across types of assets, because aggregation weights differ in the two cases.

The SNA, in its asset classification, distinguishes between dwellings and other buildings and structures as part of produced assets and land as a non-produced asset. Other buildings and structures are, in turn broken down into non-residential buildings, other structures and land improvement. Although land is a non-produced asset, it is well established in the economic literature as a factor of production and therefore as an asset that provides a flow of capital services into production.

The purpose of this chapter is to present, at some detail, the formal model behind capital measures. Although theoretical, this presentation is targeted towards implementation, i.e. it takes account of issues such as valuation of flows at mid-period prices that are relevant for national accounts and which sometimes complicate an algebraic presentation. At the same time, these considerations are indispensable for implementation of capital services measures. This part of the Manual starts out with a chapter on the derivation of user costs and its elements, the return to capital, depreciation and revaluation. It continues with the price-volume split of the value of capital services and finishes with capital measures in balance sheets.

National accounts never work with individual assets but with cohorts. Individual assets inside a cohort are similar (ideally identical) in their specifications, were installed at the same time but exhaust their individual productive capacities over different service lives. In what follows, all variables relate to cohorts of assets, not to individual assets.

This Annex uses the formulae worked out in chapter 19 and presents them in a typical sequence of implementation. An artificial but not unrealistic dataset is used to demonstrate implementation. The purpose of this annex is to document the sequence of implementation, to demonstrate how to aggregate across sectors and industries and to examine the effects of using an ex-ante versus an ex-post approach when measuring user costs. The documented dataset with all the calculations is available in spreadsheet form on [URL here]. The data set has the following features:

A full-fledged implementation of an integrated set of capital measures may be beyond the capacity of some statistical offices when, as a consequence of resourcing the statistical system, only the most basic information is available. This Annex presents a ‘minimum’ version of capital measures. Its objective is to sketch out a simplified method for capital measurement when the information basis is limited.

Investment series. Full implementation of the perpetual inventory method requires relatively long time series of gross fixed capital formation, broken down by type of asset and institutional sector or industrial activity. Such a data set may not be available. At a minimum, the following two-way classification for investment should be sought: sectoral dimension: GFCF carried out by government and by private sector and asset dimension: GFCF in machinery and equipment and in residential and non-residential structures.

This annex spells out, at some detail, the links between the age-efficiency profile and the age-price profile in the non-geometric case. A distinction is made between ageefficiency and age-price profiles for individual assets and for cohorts of assets.